Problem: Find a positive integer that is divisible by 14 and has a square root between 25 and 25.3.
Explanation: The second condition tells us that the integer must be between $25^2 = 625$ and $(25.3)^2 \approx 640$. The only multiple of 14 in this range is $\boxed{630}.$  (One easy way to find a multiple of 14 is to find a number that is both a multiple of 2 and a multiple of 7.)